Essential commutativity and spectral properties of slant Hankel operators over Lebesgue spaces

Abstract

In this paper, the commutative and spectral properties of a kth-order slant Hankel operator ( k ≥ 2, a fixed integer) on the Lebesgue space of n-dimensional torus, [Formula: see text], where [Formula: see text] is the unit circle, are studied. Characterizations for the commutativity and essential commutativity between higher order slant Hankel operators and slant Toeplitz operators have been obtained. The presence of an open disk in the point spectrum of a kth-order slant Hankel operator with a unimodular inducing function has also been ensured.